# Generalized Eigenvectors from repeated Eigenvalues

• Oct 3rd 2007, 07:48 PM
Generalized Eigenvectors from repeated Eigenvalues
Could anyone explain to me how you get the eigenvectors of the following matrix

1 2 3
0 1 4
0 0 1

I know this is a triangular matrix and the eigenvalues are 1, 1, 1 but when I check my work on matlab, it gives me the eigenvectors as [1 0 0] [-1 0 0] [1 0 0] and these are not what I calculate. I first try to find the exact eigenvector and get [a 0 0] then I set the (A-(lamdai)I) equation equal to the exact eigenvector I got to find the first generalized eigenvector. What am I doing wrong? Thanks!
• Oct 4th 2007, 12:24 AM
Opalg
Quote:

Originally Posted by rustybladz
Could anyone explain to me how you get the eigenvectors of the following matrix

1 2 3
0 1 4
0 0 1

I know this is a triangular matrix and the eigenvalues are 1, 1, 1 but when I check my work on matlab, it gives me the eigenvectors as [1 0 0] [-1 0 0] [1 0 0] and these are not what I calculate. I first try to find the exact eigenvector and get [a 0 0] then I set the (A-(lamdai)I) equation equal to the exact eigenvector I got to find the first generalized eigenvector. What am I doing wrong? Thanks!

It looks as though it's matlab that's wrong, not you. There is a triple eigenvalue $\displaystyle \lambda=1$, but only a one-dimensional eigenspace, namely multiples of [1 0 0]. Matlab is giving you this vector three times over.

You are following the correct procedure for finding the generalised eigenvectors.